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Numerical Simulation of Turbulence-Induced Flocculation and Sedimentation in a Flocculant-Aided Sediment Retention Pond

Lee, Byung Joon;Molz, Fred

  • Received : 2014.03.27
  • Accepted : 2014.06.13
  • Published : 2014.06.30

Abstract

A model combining multi-dimensional discretized population balance equations with a computational fluid dynamics simulation (CFD-DPBE model) was developed and applied to simulate turbulent flocculation and sedimentation processes in sediment retention basins. Computation fluid dynamics and the discretized population balance equations were solved to generate steady state flow field data and simulate flocculation and sedimentation processes in a sequential manner. Up-to-date numerical algorithms, such as operator splitting and LeVeque flux-corrected upwind schemes, were applied to cope with the computational demands caused by complexity and nonlinearity of the population balance equations and the instability caused by advection-dominated transport. In a modeling and simulation study with a two-dimensional simplified pond system, applicability of the CFD-DPBE model was demonstrated by tracking mass balances and floc size evolutions and by examining particle/floc size and solid concentration distributions. Thus, the CFD-DPBE model may be used as a valuable simulation tool for natural and engineered flocculation and sedimentation systems as well as for flocculant-aided sediment retention ponds.

Keywords

Computational fluid dynamics;Flocculation;Modeling;Population balance equation;Sedimentation

References

  1. Timin T, Esmail MN. A comparative study of central and upwind difference schemes using the primitive variables. Int. J. Numer. Methods Fluids 1983;3:295-305. https://doi.org/10.1002/fld.1650030308
  2. LeVeque RJ. High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 1996;33:627-665. https://doi.org/10.1137/0733033
  3. Bushell GC, Yan YD, Woodfield D, Raper J, Amal R. On techniques for the measurement of the mass fractal dimension of aggregates. Adv. Colloid Interface Sci. 2002;95:1-50. https://doi.org/10.1016/S0001-8686(00)00078-6
  4. Turchiuli C, Fargues C. Influence of structural properties of alum and ferric flocs on sludge dewaterability. Chem. Eng. J. 2004;103:123-131. https://doi.org/10.1016/j.cej.2004.05.013
  5. Hinds WC. Aerosol technology: properties, behavior, and measurement of airborne particles, 2nd ed. New York: John Wiley & Sons Inc. 1999.
  6. Strogatz SH. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Reading: Perseus Books Publishing. 1994.
  7. Bungartz H, Wanner SC. Significance of particle interaction to the modelling of cohesive sediment transport in rivers. Hydrol. Process. 2004;18:1685-1702. https://doi.org/10.1002/hyp.1412
  8. Winterwerp JC. On the flocculation and settling velocity of estuarine mud. Cont.Shelf Res. 2002;22:1339-1360. https://doi.org/10.1016/S0278-4343(02)00010-9
  9. Maggi F, Mietta F, Winterwerp JC. Effect of variable fractal dimension on the floc size distribution of suspended cohesive sediment. J. Hydrol. 2007;343:43-55. https://doi.org/10.1016/j.jhydrol.2007.05.035
  10. Adachi Y. Dynamic aspects of coagulation and flocculation. Adv. Colloid Interface Sci. 1995;56:1-31. https://doi.org/10.1016/0001-8686(94)00229-6
  11. Miyahara K, Adachi Y, Nakaishi K, Ohtsubo M. Settling velocity of a sodium montmorillonite floc under high ionic strength. Colloids Surf. A Physicochem. Eng. Asp. 2002;196:87-91. https://doi.org/10.1016/S0927-7757(01)00798-1
  12. Sterling MC Jr, Bonner JS, Ernest AN, Page CA, Autenrieth RL. Application of fractal flocculation and vertical transport model to aquatic sol-sediment systems. Water Res. 2005;39:1818-1830. https://doi.org/10.1016/j.watres.2005.02.007
  13. Ding A, Hounslow MJ, Biggs CA. Population balance modelling of activated sludge flocculation: investigating the size dependence of aggregation, breakage and collision efficiency. Chem. Eng. Sci. 2006;61:63-74. https://doi.org/10.1016/j.ces.2005.02.074
  14. Parker DS, Kaufman WJ, Jenkins D. Floc breakup in turbulent flocculation processes. J. Sanit. Eng. Div. 1972;98:79-99.
  15. Langseth JO, Tveito A, Winther R. On the convergence of operator splitting applied to conservation laws with source terms. SIAM J. Numer. Anal. 1996;33:843-863. https://doi.org/10.1137/0733042
  16. Aro CJ, Rodrigue GH, Rotman DA. A high performance chemical kinetics algorithm for 3-D atmospheric models. Int. J. High Perform. Comput. Appl. 1999;13:3-15. https://doi.org/10.1177/109434209901300101
  17. Badrot-Nico F, Brissaud F, Guinot V. A finite volume upwind scheme for the solution of the linear advection-diffusion equation with sharp gradients in multiple dimensions. Adv. Water Resour. 2007;30:2002-2025. https://doi.org/10.1016/j.advwatres.2007.04.003
  18. Durran DR. Numerical methods for wave equations in geophysical fluid dynamics. New York: Springer; 1999.
  19. Rogers SE, Kwak D. An upwind differencing scheme for the incompressible Navier-Strokes equations. Washington, DC: National Aeronautics and Space Administration; 1988.
  20. Alhumaizi K. Comparison of finite difference methods for the numerical simulation of reacting flow. Comput. Chem. Eng. 2004;28:1759-1769. https://doi.org/10.1016/j.compchemeng.2004.02.032
  21. White FM. Viscous fluid flow. 2nd ed. New York: McGraw-Hill; 1991.
  22. Heath AR, Koh PT. Combined population balance and CFD modelling of particle aggregation by polymeric flocculant. Proceedings of the 3rd International Conference on CFD in the Minerals and Process Industries; 2003 Dec 10-12; Melbourne, Australia.
  23. Lian G, Moore S, Heeney L. Population balance and computational fluid dynamics modelling of ice crystallisation in a scraped surface freezer. Chem. Eng. Sci. 2006;61:7819-7826. https://doi.org/10.1016/j.ces.2006.08.075
  24. Schwarzer HC, Schwertfirm F, Manhart M, Schmid HJ, Peukert W. Predictive simulation of nanoparticle precipitation based on the population balance equation. Chem. Eng. Sci. 2006;61:167-181. https://doi.org/10.1016/j.ces.2004.11.064
  25. Stokes GG. Mathematical and physical papers (Vol. 1). Cambridge: Cambridge University Press; 1880.
  26. Brown PP, Lawler DF. Sphere drag and settling velocity revisited. J. Environ. Eng. 2003;129:222-231. https://doi.org/10.1061/(ASCE)0733-9372(2003)129:3(222)
  27. Jiang Q, Logan BE. Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. Technol. 1991;25:2031-2038. https://doi.org/10.1021/es00024a007
  28. Johnson CP, Li X, Logan BE. Settling velocities of fractal aggregates. Environ. Sci. Technol. 1996;30:1911-1918. https://doi.org/10.1021/es950604g
  29. Spicer PT, Pratsinis SE, Raper J, Amal R, Bushell G, Meesters G. Effect of shear schedule on particle size, density, and structure during flocculation in stirred tanks. Powder Technol. 1998;97:26-34. https://doi.org/10.1016/S0032-5910(97)03389-5
  30. Flesch JC, Spicer PT, Pratsinis SE. Laminar and turbulent shear-induced flocculation of fractal aggregates. AIChE J. 1999;45:1114-1124. https://doi.org/10.1002/aic.690450518
  31. Chakraborti RK, Atkinson JF, Van Benschoten JE. Characterization of alum floc by image analysis. Environ. Sci. Technol. 2000;34:3969-3976. https://doi.org/10.1021/es990818o
  32. Chakraborti RK, Gardner KH, Atkinson JF, Van Benschoten JE. Changes in fractal dimension during aggregation. Water Res. 2003;37:873-883. https://doi.org/10.1016/S0043-1354(02)00379-2
  33. McGraw R. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 1997;27:255-265. https://doi.org/10.1080/02786829708965471
  34. Somasundaran P, Runkana V. Modeling flocculation of colloidal mineral suspensions using population balances. Int. J. Miner. Process. 2003;72:33-55. https://doi.org/10.1016/S0301-7516(03)00086-3
  35. Marchisio DL, Vigil RD, Fox RO. Quadrature method of moments for aggregation-breakage processes. J. Colloid Interface Sci. 2003;258:322-334. https://doi.org/10.1016/S0021-9797(02)00054-1
  36. Rahmani NH, Dabros T, Masliyah JH. Evolution of asphaltene floc size distribution in organic solvents under shear. Chem. Eng. Sci. 2004;59:685-697. https://doi.org/10.1016/j.ces.2003.10.017
  37. Prat OP, Ducoste JJ. Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics. Chem. Eng. Sci. 2006;61:75-86. https://doi.org/10.1016/j.ces.2004.11.070
  38. Runkana V, Somasundaran P, Kapur PC. A population balance model for flocculation of colloidal suspensions by polymer bridging. Chem. Eng. Sci. 2006;61:182-191. https://doi.org/10.1016/j.ces.2005.01.046
  39. Lee DG, Bonner JS, Garton LS, Ernest AN, Autenrieth RL. Modeling coagulation kinetics incorporating fractal theories: a fractal rectilinear approach. Water Res. 2000;34:1987-2000. https://doi.org/10.1016/S0043-1354(99)00354-1
  40. Fox RO. Computational models for turbulent reacting flows. Cambridge: Cambridge University Press; 2003.
  41. Marchisio DL, Vigil RD, Fox RO. Implementation of the quadrature method of moments in CFD codes for aggregation-breakage problems. Chem. Eng. Sci. 2003;58:3337-3351. https://doi.org/10.1016/S0009-2509(03)00211-2
  42. Kumar S, Ramkrishna D. On the solution of population balance equations by discretization: I. A fixed pivot technique. Chem. Eng. Sci. 1996;51:1311-1332. https://doi.org/10.1016/0009-2509(96)88489-2
  43. Ramkrishna D, Mahoney AW. Population balance modeling: promise for the future. Chem. Eng. Sci. 2002;57:595-606. https://doi.org/10.1016/S0009-2509(01)00386-4
  44. Gowdy W, Iwinski SR, Woodstock G. Removal efficiencies of polymer enhanced dewatering systems. Proceedings of the 9th Biennial Conference on Stormwater Research & Watershed Management; 2007 May 2-3; Orlando, FL.
  45. Harper HH. Current research and trends in alum treatment of stormwater runoff. Proceedings of the 9th Biennial Conference on Stormwater Research & Watershed Management; 2007 May 2-3; Orlando, FL.
  46. Kang JH, Li Y, Lau SL, Kayhanian M, Stenstrom MK. Particle destabilization in highway runoff to optimize pollutant removal. J. Environ. Eng. 2007;133:426-434. https://doi.org/10.1061/(ASCE)0733-9372(2007)133:4(426)
  47. Akan AO, Houghtalen RJ. Urban hydrology, hydraulics, and stormwater quality. Hoboken: John Wiley & Sons; 2003.
  48. Smoluchowski MV. Versuch einer mathematischen theorie der koagulationskinetik kolloider Losungen. Z. Phys. Chem. 1917;92:129-168.
  49. Lawler DF, Wilkes DR. Flocculation model testing; particle sizes in a softening plant. J. Am. Water Works Assoc. 1984;76:90-97.
  50. Hounslow MJ, Ryall RL, Marshall VR. A discretized population balance for nucleation, growth, and aggregation. AIChE J. 1988;34:1821-1832. https://doi.org/10.1002/aic.690341108
  51. Spicer PT, Pratsinis SE. Shear-induced flocculation: the evolution of floc structure and the shape of the size distribution at steady state. Water Res. 1996;30:1049-1056. https://doi.org/10.1016/0043-1354(95)00253-7
  52. Spicer PT, Pratsinis SE. Coagulation and fragmentation: universal steady-state particle-size distribution. AIChE J. 1996;42:1612-1620. https://doi.org/10.1002/aic.690420612

Cited by

  1. Flocculation kinetics and hydrodynamic interactions in natural and engineered flow systems: A review vol.21, pp.1, 2016, https://doi.org/10.4491/eer.2015.086

Acknowledgement

Supported by : Natural Resources Conservation Service